Energy stable scheme for random batch molecular dynamics.

The computational bottleneck of molecular dynamics is pairwise additive long-range interactions between particles. The random batch Ewald (RBE) method provides a highly efficient and superscalable solver for long-range interactions, but the stochastic nature of this algorithm leads to unphysical self-heating effect during the simulation. We propose an energy stable scheme (ESS) for particle systems by employing a Berendsen-type energy bath. The scheme removes the notorious energy drift, which exists due to the force error even when a symplectic integrator is employed. Combining the RBE with the ESS, the new method provides a perfect solution to the computational bottleneck of molecular dynamics at the microcanonical ensemble. Numerical results for a primitive electrolyte and all-atom pure water systems demonstrate the attractive performance of the algorithm, including its dramatically high accuracy, linear complexity, and overcoming the energy drift for long-time simulations.